Limit cycle oscillations arise in many natural systems such as machine tool, brain electrical signals, return on stock, electrocardiogram, earthquake, vibrations of mechanical structures (such as bridges, airplane wings, automobile engines and suspensions among others) and communication networks, for example.
Chatter, a type of limit cycle oscillation, is a self-excited relative vibration between the workpiece and the cutting tool in common machining processes such as turning process on a lathe as described in Zhang, H., Ni, J. and Shi, H., "Machining Chatter Suppression by Means of Spindle Speed Variation", PROC. S.M. WU SYMPOSIUM, Vol. 1, pp. 161-175, 1994.
The development of chatter causes a machining process to become unstable. This can result in poor surface finish, accuracy and reduced tool and other machine part life. Having to control machine tool chatter after it arises by traditional means such as by reducing spindle speed restricts the amount of material that can be removed in a turning process, for example. Therefore, development of chatter in a machining process reduces productivity and quality.
The three major approaches to chatter prediction are described in Minis, I. E., Magrab, E. B. and Pandelidis, I. O., "Improved Methods for the Prediction of Chatter in Turning, Part 3: A Generalized Linear Theory", ASME Journal of Engineering for Industry, vol. 112, pp. 28-35, 1990; Tansel, I. N. et. al, "Recognition of Chatter With Neural Networks," INT. J. MACH. TOOLS MANUFACT., vol. 31, No. 4, pp. 539-552, 1991; and the U.S. patent to Delio entitled "Method of Controlling Chatter in a Machine Tool," U.S. Pat. No. 5,170,358.
The presence and evolution of chatter can be monitored by measuring the vibration signals from the cutting tool using appropriately placed accelerometers. Such a signal is called the "chatter signal." The chatter signal can be analyzed to discern the state of the machining process. A conceptual model of the chatter signal generation is shown in FIG. 1. As is clear, the chatter signal, X(t), will be a complicated random signal.
The three approaches to manufacturing operations of relevance to chatter phenomenon can be categorized as (1) Prevent Approach (leads to conservative operational ratings and resultant low throughput); (2) Detect and Control Approach (leads to reworking or scrapping workpieces and resultant low quality and throughput); and (3) Predict and Prevent Approach (leads to optimal high operational ratings and resultant high quality and high throughput).